Units and Measurement - The Physics Hub

Measurement is the process of determining the size, quantity, or degree of something.
Every measurement consists of two parts:
- Magnitude (numerical value)
- Unit (standard reference)

Physical quantities are quantities that can be measured, and they are classified into two types:
- Fundamental Quantities: These cannot be defined in terms of other quantities (e.g., mass, length, time).
- Derived Quantities: These are derived from fundamental quantities (e.g., speed = distance/time).

The International System of Units (SI) is the globally accepted system for measurements.
The seven base SI units are:
1. Length – meter (m)
2. Mass – kilogram (kg)
3. Time – second (s)
4. Electric current – ampere (A)
5. Temperature – kelvin (K)
6. Amount of substance – mole (mol)
7. Luminous intensity – candela (cd)

The dimension of a physical quantity shows how and in what powers the fundamental quantities are involved.
For example:
- Force (F) = Mass × Acceleration → [M^1L^1T^(-2)]
Dimensional analysis is used to derive formulas and check the consistency of equations.

Early methods of measurement used human body parts, but today, standard units are used for accuracy and precision.
Standardization is crucial, as non-standard measurements can lead to errors.

Accuracy refers to how close a measured value is to the true value.
Precision refers to how close multiple measurements of the same quantity are to each other.
Errors are deviations from the true value and can be:
- Systematic errors (consistent in a particular direction)
- Random errors (caused by unpredictable factors)
- Absolute error: Difference between the measured value and the true value.
- Relative error: Absolute error divided by the true value.
- Percentage error: (Relative error × 100%).

Significant figures are the digits in a measurement that are meaningful in terms of precision.
Rules for counting significant figures:
1. Non-zero digits are always significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros (before non-zero digits) are not significant.
4. Trailing zeros in a decimal number are significant.

Some quantities require derived units, e.g., speed (m/s), acceleration (m/s²), force (N), work (J), power (W), etc.
Composite units are combinations of two or more units, e.g., m/s for velocity, kg/m³ for density.

Unit conversion is important to ensure consistency in measurements across different systems.
A unit conversion factor is used to convert one unit to another (e.g., 1 km = 1000 m).

Scalar quantities have only magnitude (e.g., mass, time).
Vector quantities have both magnitude and direction (e.g., velocity, force).

Understand and memorize the SI units and their corresponding prefixes.
Practice converting units and solving problems based on dimensional analysis.
Focus on error analysis and how it applies to experimental data.
Study significant figures in-depth, as many problems involve precision in measurements.
Use dimensional formulas to check the correctness of equations in physics.
Know the difference between scalars and vectors and how to handle both in problem-solving.